Interferometric Measurement of the Diameter of a Silicon Sphere With a Mechanical Scanning Method

The diameter of a 1-kg silicon sphere needs to be accurately measured to determine the volume and density to investigate the Avogadro constant. The diameter of the silicon sphere was measured using phase-shifting interferometry with an algorithm with an accuracy of 0.01% of the phase period. The algorithm accurately analyzes the phase map without strict positioning of the phase-shifting step. A phase-shifting generator was then designed to accurately determine the diameter. The distances between the two Etalon plates were measured with a phase shift of 1 μm with the gaps between the surface of the silicon sphere and each Etalon plate measured with a phase shift of 2 μm by the mechanical scanning method. The Etalon cavity length changes by only 0.1 nm when the pressure is released. The combined standard uncertainty in the silicon sphere diameter is then less than 2.3 nm.